Properties

Base field \(\Q(\sqrt{6}) \)
Label 2.2.24.1-96.1-d
Conductor 96.1
Rank not recorded

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Base field \(\Q(\sqrt{6}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 6 \); class number \(1\).

Elliptic curves in class 96.1-d over \(\Q(\sqrt{6}) \)

Isogeny class 96.1-d contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
96.1-d1 \( \bigl[a\) , \( a + 1\) , \( a\) , \( -135 a - 335\) , \( 2080 a + 5094\bigr] \)
96.1-d2 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -40 a + 98\) , \( -198 a + 485\bigr] \)
96.1-d3 \( \bigl[0\) , \( 1\) , \( 0\) , \( -2\) , \( 0\bigr] \)
96.1-d4 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -86 a - 210\) , \( -774 a - 1896\bigr] \)
96.1-d5 \( \bigl[a\) , \( a + 1\) , \( a\) , \( -160 a - 395\) , \( 1485 a + 3636\bigr] \)
96.1-d6 \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 135 a - 335\) , \( -2080 a + 5094\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 8 & 2 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 2 & 4 & 2 & 4 & 1 & 2 \\ 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph